Question

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

2.$\left[\begin{array}{ccc}1& 2& 3\\ 1& 6& 8\\ -2& -4& 0\end{array}\right]$

Short answer

Therefore, the determinant of given matrix is given by,

$detA=24$

Step-by-step solution

Definition

Gaussian elimination method is used to solve a system of linear equations.

Gaussian elimination provides a relatively efficient way of constructing the inverse to a matrix.

Interchanging two rows. Multiplying a row by a constant (any constant which is not zero).

Given

Given Matrix,

$A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 6& 8\\ -2& -4& 0\end{array}\right]$

To find determinant by using Gaussian Eliminations

First, we multiply the first row by -1 and add it to the second row. Then, we multiply the first row by 2 and add it to the third row.

We get,

$A=\left[\begin{array}{ccc}1& 2& 3\\ 0& 4& 5\\ 0& 0& 6\end{array}\right]$

We had zero row swaps, so

role="math" localid="1659503688412" $$\begin{gathered} \det \mathrm{A}={(-1)}^0.1.4·6 \\ \det \mathrm{A}=24 \end{gathered}$$